Abstract
The paper has two principal aims. First, Pietroski's sparse account of semantic composition will be favourably compared to the familiar full Frege hierarchy of composed semantic types. Second, I shall introduce the idea of a head as employed in linguistics and pose the problem of how to square Pietroski's compositional principles with the asymmetry entailed by headedness. The paper will leave the problem of headedness as an outstanding issue to be resolved.
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